Four-year-old Mariamma was reciting number names - some of them in order, and others randomly. The child's aunt, sitting nearby, asked her, "Can you write 'two'?" She said she could, and wrote the following:
When her aunt asked what she had drawn alongside, the child replied, "Ducks." On asking her why she had drawn them, she replied, "This is the way two is written in the book." Then her aunt wrote '2 0 0', and asked if this was two.
Mariamma replied that it wasn't.
It is quite clear that Mariamma had no idea that 'two' refers to any collection of two objects. Can we then say that she had a concept of number, even though she could write the numerals from 1 to lo?
What does help a child to develop the ability to count is to introduce counting using real objects. Let the child try and understand the meaning of 'two', say, by showing her two leaves, two pencils, two books, clapping twice, and so on.
Each time stress the word 'two'. From these experiences the child will gradually understand that what all the groups of two objects have in common is the quality 'two'
In this way we can help them understand numbers upto five, not necessarily in the usual order. For example, they could learn them in the order - 'one'; 'two', 'five', 'three', 'four'. They can learn the conventional order later, which will help them conceptualise bigger and bigger numbers. At each stage we can ask them questions like - how many marbles do I have? How many times did I hop? Which four of you are going to come to the board? And SO on.
But, a word of caution! When counting objects for the child, we usually move from one object to the next, saying "one, two, three", and so on, as we touch each object. The child sees the adult touching these items, and saying a different word for each one. She may conclude that 'one', 'two', and 'three' are names of these objects, as happened in Example 2, described earlier. We do not explain to the child that we called the second object 'two' because we assumed that we are now referring t-o a collection of two objects the object that we touched earlier and the one we are touching now. Just because we understand this, we expect the child to understand this too. In fact, we do not even realise that the child may be getting confused.
This confusion can be avoided if counting is introduced by counting a variety of objects or actions on various occasions and in different Orders. One could also touch the first object and say, "This is one leaf', and move it to another side. Then take the second one and move it towards the first one, and say, "This is one more. So now there are two leaves." Continue in this way. This kind of exercise should be done with stacks balls, stones, and so on. It can also be done with actions. For example, you can clap once and say, "Now, I have clapped my hands one time." Then you can clap twice and say, "Now have clapped two times", and so on. In this way it becomes clear that the number name refers not to a particular object or action, but to the size of the group of objects (or actions) that we have set to one side. This also helps the child to know that there is a sequencing of numbers in which the subsequent number is one more than the previous one.
There is another aspect that is important to remember when introducing number names. When using objects for teaching counting, we tend to arrange them in a fixed pattern for a particular number name each time. For example, we usually tend to arrange two pebbles as'.', three pebbles as two and four pebbles as Here the child may begin to think that it is something about the arrangement of objects that is called 'two', 'three', 'four', and so on. So, for instance, this child may say that 0.0 is two pebbles. This problem can be avoided if we keep changing the patterns. Thus, when showing three objects, on one occasion we may put them in a row, on another as a triangle. Four objects could be arranged as
Why don't you try an exercise now?